A specific initial amplitude in the signum-Gordon model generates a spectral mass of unity whose dispersion matches the massive Klein-Gordon equation.
A New Approach to Integrable Theories in any Dimension
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abstract
The zero curvature representation for two dimensional integrable models is generalized to spacetimes of dimension d+1 by the introduction of a d-form connection. The new generalized zero curvature conditions can be used to represent the equations of motion of some relativistic invariant field theories of physical interest in 2+1 dimensions (BF theories, Chern-Simons, 2+1 gravity and the CP^1 model) and 3+1 dimensions (self-dual Yang-Mills theory and the Bogomolny equations). Our approach leads to new methods of constructing conserved currents and solutions. In a submodel of the 2+1 dimensional CP^1 model, we explicitly construct an infinite number of previously unknown nontrivial conserved currents. For each positive integer spin representation of sl(2) we construct 2j+1 conserved currents leading to 2j+1 Lorentz scalar charges.
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hep-th 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Reformulating 1+1D Yang-Mills with matter fields via holonomies produces an infinite hierarchy of gauge-invariant conserved charges that generate symmetries preserving the dynamics and are in involution when a boundary constant lies in the gauge group center.
Gauge-invariant charge densities for the 1-instanton are defined via non-Abelian magnetic and electric fluxes through spheres, yielding non-zero values at r=1 for both instanton and anti-instanton.
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Signum-Gordon spectral mass from nonlinear Fourier mode mixing
A specific initial amplitude in the signum-Gordon model generates a spectral mass of unity whose dispersion matches the massive Klein-Gordon equation.
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The Hidden Symmetries of Yang-Mills Theory in (1+1)-dimensions
Reformulating 1+1D Yang-Mills with matter fields via holonomies produces an infinite hierarchy of gauge-invariant conserved charges that generate symmetries preserving the dynamics and are in involution when a boundary constant lies in the gauge group center.
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On the gauge-invariant dynamical charges and densities of the 1-instanton solution
Gauge-invariant charge densities for the 1-instanton are defined via non-Abelian magnetic and electric fluxes through spheres, yielding non-zero values at r=1 for both instanton and anti-instanton.